Discrete Event Simulation for Health Economic Modelling

John A. Graves, Ph.D.

Professor of Health Policy and Medicine, Vanderbilt University School of Medicine

Professor of Management, Vanderbilt Owen Graduate School of Management

Director, Vanderbilt Center for Health Economic Modeling

Overview

1. Conceptual Issues

  • A (brief) overview of decision modelling approaches.
  • A taxonomy of errors in decision modelling.
  • What does DES buy you?
  • Basic terminology and visualisation of DES.

2. Computational Issues

  • Computational considerations for DES.
  • A worked example of DES for health economic modelling.

A (brief) overview of decision modelling approaches

Deterministic Models





Cohort-level models that track expected values.

Deterministic Models

  1. Discrete Time Markov Cohort
  • Characterized by transitions among mutually exclusive health states.
  • Suffers from “memoryless” property, though tricks can help.
  • Useful for expected outcomes, though possible to analytically solve for higher-order moments, e.g., variance, skewness; see Caswell and van Daalen (2021).

Deterministic Models

  1. Differential equations modelling
  • Draws on stochastic process theory.
  • Processes represented by differential equations (DEQs).
  • Solutions to DEQs provide occupancy of underlying process at time t.

Stochastic Models





Individual-level models that simulate patient pathways with random variation.

Stochastic Models

  1. Microsimulation

    • An individual state-transition model (STM).
    • Facilitate transition probabilities that are a function of attributes. (e.g., time since disease onset, the occurrence of previous events, or time-varying response to treatment).
    • Can capture greater scope of output since the model returns the distribution of events.

Stochastic Models

  1. Discrete Event Simulation
  • Extends the flexibilities of microsimulation.
  • Models time to event(s) explictly.
  • Can incorporate interdependencies and resource contention (e.g., wait times, queueus)

A Taxonomy of Modelling Error

Unavoidable (Shared) Errors





Inherent errors you (generally) cannot minimize or sidestep by choosing a specific modelling approach.

Errors in Expectation

  • Structural errors that result in bias.
  • Attributes of models / parameters that result in model estimates that deviate from the “true” underlying event generation process.
  • Not the same as heterogeneity!

Errors in Expectation

  • Structural errors that result in bias..
  • Attributes of models / parameters that result in model estimates that deviate from the “true” underlying event generation process.
  • Not the same as heterogeneity!

Biases in outcomes due to unmodelled queues / resource contention can be addressed using DES!

Errors in Expectation

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural

Estimation Errors

  • Sampling and estimation uncertainty.
  • Focus of VOI.

Estimation Errors

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural
Estimation and sampling

Addressable Errors





Errors you can address using specific methods and approaches.

Can minimize or sidestep by choosing a specific modelling approach.

Integration Error

  • Occurs when events accumulate at cycle boundaries.
  • Easily corrected with 1/2 cycle correction, Simpson’s rule approaches, etc.

Integration Error

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural
Estimation and sampling
Integration

Stochastic Error

  • Realisation and timing of events among otherwise identical patients may vary.
  • Literature refers to this as “first-order” uncertainty.
  • Can be addressed by increasing simulated patient sample M.

Stochastic Error

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural
Estimation and sampling
Integration
Stochastic

Embedding Error

  • Standard rate-to-probability conversion formulas (i.e., P = 1 - e^{-rt}) only accurate if no competing events.
  • Pairwise conversions will effectively rule out the possibility of 2 or more events in same cycle.
  • Easily addressed by embedding transition probability matrix \mathbf{P} using matrix analogue to standard formula, i.e., \mathbf{P} = \exp{(\mathbf{R}t}).
  • See Leech et al. (2025) and Graves et al. (2021) for techniques.

Embedding Error

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural
Estimation and sampling
Integration
Stochastic
Embedding

Truncation Error

  • Information on the precise timing of an event occurring in continuous time is lost when event times are moved to the cycle boundary point.
  • Analogue: loss of power when dichotomizing a continuous variable.

Information Loss in Discrete Time

Information Loss in Discrete Time

Information Loss in Discrete Time

Truncation Error vs. Integration Error

  • Integration error affects expected values.
  • Truncation error affects variance.
  • Addressable by increasing simulated patient size M or decreasing cycle length.

Truncation Error

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural
Estimation and sampling
Integration
Stochastic
Embedding
Truncation

What does DES buy you?

Deterministic Models
Stochastic Models
Error Type DEQ MRKCHRT MICROSIM DES
Structural ✓ (-queues)
Estimation and sampling
Integration
Stochastic
Embedding
Truncation

What Does DES Buy You?

  • No embedding error because event times are randomly sampled based on rates.
  • No truncation error because exact event times used.
  • DES will converge much faster than microsimulation.

What Does DES Buy You?

  • Can explicitly model wait times and resource contention.
  • Technical demands (roughly) on par with microsimulation.

References

Caswell, Hal, and Silke van Daalen. 2021. “Healthy Longevity from Incidence-Based Models: More Kinds of Health Than Stars in the Sky.” Demographic Research 45 (July): 397–452. https://doi.org/10.4054/demres.2021.45.13.
Graves, John, Shawn Garbett, Zilu Zhou, Jonathan S Schildcrout, and Josh Peterson. 2021. “Comparison of Decision Modeling Approaches for Health Technology and Policy Evaluation.” Medical Decision Making 41 (4): 453–64.
Leech, Ashley A, Jinyi Zhu, Hannah Peterson, Marie H Martin, Grace Ratcliff, Shawn Garbett, and John A Graves. 2025. “Modeling Disability-Adjusted Life-Years for Policy and Decision Analysis.” Medical Decision Making, 0272989X251340077.